An electrician sent Bonnie an invoice in the amount of 'a' dollars for 6 hours of work that was done on Saturday. The electrician charges a weekend fee 'f' in addition to an hourly rate 'r'. Bonnie knows what the weekend fee is. Write a formula Bonnie can use to find 'r', the rate the electrician charges per hour.

Answer:

[tex]0.017y=0.017x+0.97[/tex]

Step-by-step explanation:

Let us assume that,

number of minutes read by Kiran is = x minutes.

number of minutes read by Andre is = y minutes.

Andre read for 58 minute more than that of Kiran.

Converting minute to hour we get,

[tex]x\text{ minutes}=\dfrac{x}{60}=0.017x\text{ hour}[/tex]

[tex]y\text{ minutes}=\dfrac{y}{60}=0.017y\text{ hour}[/tex]

[tex]58\text{ minutes}=\dfrac{58}{60}=0.97\text{ hour}[/tex]

So the relationship between x and y will be,

[tex]0.017y=0.017x+0.97[/tex]

To relate the number of minutes Kiran read with the number of minutes Andre read, we can use the equation y = x + 58, where x is the number of minutes Kiran read.

To write an equation that relates the number of minutes Kiran read with y, the number of minutes that Andre read, we can use the information given. Let's say Kiran read for x minutes. According to the question, Andre read for 58 more than that, so we can represent Andre's reading time as x + 58. Therefore, the equation would be y = x + 58.

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1.  -3(2x-3) = 25-8x is given.

2.  -6x+9 = 25-8x  simplified the left hand side

3. 2x+9 = 25 eft hand side of the equation and simplified

4. 2x = 16 equation are brought to the right side of the equation and simplified

5.  the whole equation is divided by 2 in order to get the value of 'x' i.e. x = 8.

We are provided with an equation and are required to give reasons on how we got the final answer.

(1.) The equation is -3(2x-3) = 25-8x is given.

(2.) In this step, we have simplified the left hand side of the equation by opening the bracket i.e. -6x+9 = 25-8x

(3.) Here, the terms containing 'x' are brought to the left hand side of the equation and simplified i.e. 2x+9 = 25

(4.) Now, the constant terms of the equation are brought to the right side of the equation and simplified i.e. 2x = 16.

(5.) Lastly, the whole equation is divided by 2 in order to get the value of 'x' i.e. x = 8.

Answer:

The graph of y = 6x increases at a faster rate than the graph of y = 2x.

Step-by-step explanation:

y=6x and y=2x are proportional relationships of linear functions. It has the form y=mx where m is the rate of change or increase. 6>2 so y=6x will increase faster than 2.

We know the last two statements are not possible because a translation of a graph must be done through addition or subtraction.

[tex]a,b-the\ numbers\\\\a-b=34\to a=34+b\\\\a^2+b^2\to minimum\\\\\text{substitute:}\\\\(34+b)^2+b^2\to minimum\\\\f(b)=(34+b)^2+b^2\qquad\text{use}\ (x+y)^2=x^2+2xy+y^2\\\\f(b)=34^2+(2)(34)(b)+b^2+b^2\\\\f(b)=1156+68b+2b^2\to f(b)=2b^2+68b+1156\\\\y=ax^2+bx+c\\\\if\ a>0\ then\ a\ parabola\ op en\ up\\if\ a<0\ then\ a\ parabola\ op en\ down\\\\if\ a>0\ then\ a\ parabola\ has\ a\ minimum\ at\ a\ vertex\\if\ a<0\ then\ a\ parabola\ has\ a\ maximum\ at\ a\ vertex[/tex]

[tex]\text{We have}\ a=2>0.\ \text{Therefore the parabola has the minimum at the vertex.}\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a};\ k=f(h)\\\\\text{We have}\ a=2\ \text{and}\ b=68.\ \text{Substitute:}\\\\h=\dfrac{-68}{2(2)}=\dfrac{-68}{4}=-17\\\\k=f(-17)=2(-17)^2+68(-17)+1156=2(289)-1156+1156=578[/tex]

[tex]\text{Therefore}\ b=-17\ \text{and}\ a=34+b\to a=34+(-17)=17.\\\\Answer:\ a^2+b^2=17^2+(-17)^2=289+289=578[/tex]

The minimum sum of their squares is [tex]\(578\)[/tex].The sum of their squares is a minimum when each number is half the difference between them.The sum of their squares is[tex]\(2 \times \left(\frac{34}{2}\right)^2\)[/tex].

Let the two numbers be [tex]\(x\)[/tex] and [tex]\(y\)[/tex], where [tex]\(x > y\)[/tex]. Given that the difference between the numbers is 34, we can express [tex]\(y\)[/tex] in terms of [tex]\(x\) as \(y = x - 34\)[/tex].

We want to find the minimum value of the sum of their squares, which is [tex]\(x^2 + y^2\)[/tex]. Substituting [tex]\(y\)[/tex] with [tex]\(x - 34\)[/tex], we get:

[tex]\[S = x^2 + (x - 34)^2\] \[S = x^2 + x^2 - 68x + 1156\] \[S = 2x^2 - 68x + 1156\][/tex]

To find the minimum value of [tex]\(S\)[/tex], we take the derivative of [tex]\(S\)[/tex] with respect to [tex]\(x\)[/tex] and set it equal to zero:

[tex]\[\frac{dS}{dx} = 4x - 68\][/tex]

Setting the derivative equal to zero gives us:

[tex]\[4x - 68 = 0\] \[x = \frac{68}{4}\] \[x = 17\][/tex]

Since [tex]\(y = x - 34\)[/tex], we substitute [tex]\(x = 17\)[/tex] to find [tex]\(y\)[/tex]:

[tex]\[y = 17 - 34\] \[y = -17\][/tex]

So the two numbers are 17 and -17. The sum of their squares is:

[tex]\[17^2 + (-17)^2 = 289 + 289\] \[= 578\][/tex]

However, since we are looking for the minimum sum of squares, we can also use the property that the sum of squares is minimum when the numbers are equidistant from their mean. The mean of the two numbers is [tex]\(\frac{34}{2}\)[/tex], so the numbers would be [tex]\(\frac{34}{2}\)[/tex] and [tex]\(-\frac{34}{2}\)[/tex]. The sum of their squares is:

[tex]\[2 \times \left(\frac{34}{2}\right)^2 = 2 \times 289\] \[= 578\][/tex]

Answer:

Concentration of solution A = 23%

and concentration of solution B = 2%

Step-by-step explanation:

Lets get started

lets say that we concentration of solution A be x% and concentration of second solution be y%

we also know that first mixture is obtained by mixing them in ratio of 2:7

so linear equation representing this situation can be written as:

2(x%)+7(y%)= 9(6.66%)    

changing percentage to decimal we get,

.02x+.07y=9(.0666)

.02x+.07y = 0.6          (equation 1 )

similarly , second mixture is obtained by mixing them in ratio of 7:3

so linear equation can be written as:

7(x%)+3(y%) = 10(16.7%)

.07x +.03y = 1.67     (equation 2)

solving equations 1 and 2  we get

x =  23 and y = 2

so concentration of solution A = 23%

and concentration of solution B = 2%

That's the final answer

Hope it was helpful !!

Answer:

Ruth is  x+4=7/3+4,   esmerelda  is  5x+4=35/3+4

Step-by-step explanation:

if Ruth is x, esmerelda is 5x,

four years ago,

Ruth is x+4,  esmerelda is 5x+4,  depend on the sum, we get:

x+4+5x+4=22, x=7/3

so:

Ruth is  x+4=7/3+4,   esmerelda  is  5x+4=35/3+4

Answer:

 x = - 50

Step-by-step explanation:

-2/5 x - 2 = 18

-2x - 10 = 90

-2x = 100

 x = - 50

Answer:

A) -50

Step-by-step explanation:

The given equation -2/5 x - 2 = 18

Here we have to find the value of x.

Step 1: Isolate the constant.

Add 2 on both sides, we get

-2/5x - 2 + 2 = 18 +2

-2/5x = 20

Step 2: Multiply both sides by the reciprocal of -2/5

The reciprocal of -2/5 is -5/2

x = 20 * -5/2

x = -100/2

x = -50

Answer: x = -50

Hello from MrBillDoesMath!

Answer:

x = (1/2) (z + y)    

Discussion:

Solve    2x-y =z for x.

2x -y = z      =>              

2x -y + y = z + y   =>            ( add "y" to both sides)

2x = z + y

x = (1/2) (z + y)                     ( divide both sides by 2)

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

Chicken=97/221=0.44

Cow=47/221=0.21

Human=77/221=0.35

Step-by-step explanation:

Answer:

[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]

Step-by-step explanation:

To write sin6x-sinx  as a product , we use formula

[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]

We have 6x in the place of 'a'  and x in the place of b

Replace it in the formula

[tex]sin(a) - sin(b)= 2cos(\frac{a+b}{2}) * sin(\frac{a-b}{2})[/tex]

[tex]sin(6x) - sin(x)= 2cos(\frac{6x+x}{2}) * sin(\frac{6x-x}{2})[/tex]

[tex]sin(6x) - sin(x)= 2cos(\frac{7x}{2}) * sin(\frac{5x}{2})[/tex]

The answer is B.

B . The diagonals are congruent.

A. The diagonals of any rhombus bisect each other, but that does not prove it is a rectangle.

B. The quadrilateral is a parallelogram, and the diagonals are congruent. It must be a rectangle.

C. The diagonals are congruent and perpendicular in any rhombus, but that does not make it a rectangle.

D. This proves a rhombus, but not necessarily a rectangle.

Answer:

$307.5.

Step-by-step explanation:

We have been given that Elena's aunt bought her a $150 savings bond when she was born.When Elena is 20 years old, the bond will have earned 105% in interest.  

To find bond's value after 20 years we will add 105% of 150 to 150.

[tex]\text{Bond's value after 20 years}=150+(\frac{105}{100}\times 150)[/tex]

[tex]\text{Bond's value after 20 years}=150+(1.05\times 150)[/tex]

[tex]\text{Bond's value after 20 years}=150+157.5[/tex]

[tex]\text{Bond's value after 20 years}=307.5[/tex]

Therefore, the bond will be worth $307.5, when Elena will be 20 years old.

Using the formula for future value, the $150 savings bond bought for Elena that earned 105% interest by the time she's 20 years old will be worth $307.50.

The question involves calculating the future value of a savings bond when it will have earned a specific percentage in interest. In Elena's case, her aunt bought her a $150 savings bond, and this bond will have earned 105% in interest by the time Elena is 20 years old.

Calculating the future value of the bond can be done using the formula:

Future Value (FV) = Present Value (PV) × (1 + Interest Rate (i))ⁿ

For Elena's savings bond:

Inserting these values into the formula, we get:

FV = $150 × (1 + 1.05)

Therefore, the future value of the bond when Elena is 20 years old will be:

FV = $150 × 2.05

FV = $307.50

So, Elena's bond will be worth $307.50 when she is 20 years of age.

Answer:

Your answer would be C because a trinomial consists of 3 parts!

Step-by-step explanation:

Answer:

[tex]2x^3-7y^3 +14[/tex]

Step-by-step explanation:

Trinomial is a expression that has 3 terms. Now we check the options that has 3 terms.Terms are separated by operators like +,- , x or \

5xy has only one term

[tex]2x-7[/tex] has two terms 2x and -7. So it is not a trinomial

[tex]2x^3-7y^3 +14[/tex] has three terms 2x^3, -7y^3 and +14. So it is a trinomial.

[tex]2y^2+7y[/tex] has two terms, So it is not a trinomial

Answer: (D) -3 < x < 17

Step-by-step explanation:

x must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

2x + 6 > 0       and        x + 23 > 0

       x > -3       and               x > -23

To satisfy both, x > -3

Part 2: The 80° is less than the 100° so the corresponding side of 80° must also be less than the corresponding side of 100°

        80° < 100°

⇒ 2x + 6 < x + 23

      x + 6 <       23

      x       <        17

Therefore x must be between -3 and 17

⇒  -3 < x < 17

************************************************************

Answer: (C) -1.6 < y < 7

Step-by-step explanation:

y must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

4y + 15 > 0             and        5y + 8 > 0

         y > -3.75       and               y > -1.6

To satisfy both, y > -1.6

Part 2: The 60° is less than the 105° so the corresponding side of 60° must also be less than the corresponding side of 105°

        60° < 105°

⇒ 5y + 8 < 4y + 15

      y + 8 <        15

      y       <         7

Therefore y must be between -1.6 and 7

⇒  -1.6 < y < 7

************************************************************

Answer: (A) 2.4 < y < 5

Step-by-step explanation:

y must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

2y + 3 > 0       and        5y - 12 > 0

       y > -1.5       and               y > 2.4

To satisfy both, y > 2.4

Part 2: The 70° is less than the 140° so the corresponding side of 70° must also be less than the corresponding side of 140°

        70° < 140°

⇒ 5y - 12 < 2y + 3

    3y - 12 <         3

    3y       <        15

      y       <          5

Therefore y must be between 2.4 and 5

⇒  2.4 < y < 5

The percent markup is 62.5%

The work is provided in the image attached.

Final answer:

The cheerleaders can be lined up in 3,628,800 ways.

Explanation:

To solve this problem, we need to consider the arrangement of the cheerleaders in two rows of five people each. Since each cheerleader in the back row must be taller than the one immediately in front, we can start by arranging the taller cheerleaders in the back row.

There are 10 different heights, so we have 10 choices for the tallest cheerleader in the back row. After choosing the tallest cheerleader in the back row, there are 9 choices for the second tallest cheerleader, 8 choices for the third tallest cheerleader, and so on, until there are 6 choices for the shortest cheerleader in the back row.

Once we have arranged the back row, there are 5 cheerleaders left to be arranged in the front row. Since the heights of the cheerleaders in the front row are smaller than the heights of the cheerleaders in the back row, we can simply arrange them in any order. There are 5! (5 factorial) ways to arrange the cheerleaders in the front row.

Therefore, the total number of ways to line up the cheerleaders is: 10 x 9 x 8 x 7 x 6 x 5! = 10! = 3,628,800 ways.

Answer: 7 years

Step-by-step explanation:

Answer:

CN Tower = 550 m and church tower = 160 m

Step-by-step explanation:

The first equation x + y = 710 is correct

but the second one is

x - y = 390    

Note x = height of the CN tower and y = height of the church.

x + y = 710

x - y = 390

If we add the 2  above equations we eliminate y so

2x = 1100

x = 550 m

and y = 710 - 550 =  160 m

Answer:

r ≈ 0.98

Step-by-step explanation:

The correlation coefficient is easily calculated by almost any scientific or graphing calculator, or by a spreadsheet. It is mainly a matter of data entry and invoking the appropriate function. Here, the correlation coefficient is computed as about 0.97716, or 0.98 when rounded to the nearest hundredth.

Answer:

The correlation coefficient is 0.0002273427

Step-by-step explanation:

Given the data of heart rate and we have to find the correlation coefficient which can be calculated as

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2} ] [n\sum y^{2}-(\sum y)^{2} ] }} }[/tex]

       = [tex]=\frac{12(7949)-68(1341)}{\sqrt{[12(430)-4624][12(152729)-1798281]} }[/tex]

       = [tex]\frac{4200}{(536)(34467)}[/tex]

       = 0.0002273427

Answer:

(a). [tex]h=\frac{3V}{B}[/tex]

(b). 18 cm.

Step-by-step explanation:

We have been given the volume of pyramid is given by the formula [tex]V=\frac{1}{3}Bh[/tex], where B is the area of the base and h is the height.

(a). Let us solve the given formula for h as:

[tex]V=\frac{1}{3}Bh[/tex]  

Multiply both sides by [tex]3[/tex]:

[tex]3\cdotV=3\cdot\frac{1}{3}Bh[/tex]  

[tex]3V=Bh[/tex]

Divide both sides by B:

[tex]\frac{3V}{B}=\frac{Bh}{B}[/tex]

[tex]\frac{3V}{B}=h[/tex]

Switch sides:

[tex]h=\frac{3V}{B}[/tex]

(b). To find the height for the given pyramid, we will substitute the given values as:

[tex]h=\frac{3(216\text{ cm}^3)}{36\text{ cm}^2}[/tex]

[tex]h=\frac{648\text{ cm}}{36}[/tex]

[tex]h=18\text{ cm}[/tex]

Therefore, the height of the pyramid is 18 cm.

To find the inverse of the function f(x) = 2x - 5/3x + 4, swap x and y and solve for y. The inverse function is f-1(x) = (x - 4) / (2 - 5/3).

To find the inverse of a function, we need to swap the variables x and y and solve for y. Let's start:

f(x) = 2x - 5/3x + 4

Replace f(x) with y:

y = 2x - 5/3x + 4

To find the inverse, solve for x:

x = (y - 4) / (2 - 5/3)

Now, swap x and y to find the inverse function:

y = (x - 4) / (2 - 5/3)

Therefore, the inverse of f(x) = 2x - 5/3x + 4 is f-1(x) = (x - 4) / (2 - 5/3).

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Answer:

it will take 355 minutes or 5 hours 55 minutes to be half empty. An equation would be (8,520 ÷ 2) ÷12 = m

Step-by-step explanation:

First, you must find half of 8,520 to see how much will half to be left in the pool for the problem. 8,520÷2=4,260

Second, you have to divide 4,260 by twelve to find out how many minutes it will take to become half empty.

Good luck ;b

Answer:

The equation that can be used to find the number of minutes that it would take for the pool to be half full is:

M = (8,520 / 2) / 12

As a result, it would take 355 minutes for the pool to be half full.

Step-by-step explanation:

First, we must determine how many gallons the half-filled pool has. If completely filled it has a capacity of 8,520 gallons, half-filled this should have a capacity of 8,520 / 2, that is, 4,260 gallons.

Then, we must divide this amount of gallons by the gallons that are lost per minute, that is, 4,260 / 12. In this way we get the amount of minutes it takes for the pool to reach half its capacity.

Then, the equation to determine the amount of minutes (M) it takes for the pool to reach half its capacity is: M = (8,520 / 2) / 12

Answer:

Exponential Decay

Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.

Step-by-step explanation:

We can graph the function by graphing two points when x=0 and x=1.

x=0 has [tex]y=7^{-x} =7^{0} =1[/tex]

x=1 has y=[tex]7^{-x} =7^{-1} =\frac{1}{7}[/tex]

This function starts with higher output values and decreases over time. This is Exponential Decay. Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.

Using limits, it is found that since [tex]\lim_{x \rightarrow \infty} f(x) < \lim_{x \rightarrow -\infty} f(x)[/tex], it is an exponential decay function, as it starts at infinity and ends at 0.

An exponential function is modeled by:

[tex]f(x) = ab^x[/tex].

Then:

In this problem, the function is:

[tex]y = 7^{-x}[/tex]

Hence:

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 7^{-x} = 7^{-\infty} = \frac{1}{7^{\infty}} = 0[/tex]

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 7^{-x} = 7^{\infty} = \infty[/tex]

Hence, it is exponential decay, as it starts at infinity and ends at 0.

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Answer:

19

Step-by-step explanation:

19-10=9

Answer:

y < -3

Step-by-step explanation:

Isolate the variable, y. Treat the > sign like an equal sign, what you do to one side, you do to the other.

8 - 5y > 23

Do the opposite of PEMDAS (Parenthesis, Exponent (& roots), Multiplication, Division, Addition, Subtraction).

First, subtract 8 from both sides

8 (-8) - 5y > 23 (-8)

-5y > 23 - 8

-5y > 15

Isolate the variable. Divide -5 from both sides. Note that when dividing a negative number from both sides, you must flip the sign.

(-5y)/-5 > (15)/-5

y < 15/-5

y < -3

y < -3 is your answer

~

Answer:

392 ft

Step-by-step explanation:

Hello, Let me help you with this

to find the real length and width you can use a rule of three

Step 1

length=8 in

Let

if

2.5 in ⇔ 35 ft

8 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{8\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=8\ in\\x*2.5\ in=8\ in *35\ feet\\x=\frac{8\ in *35\ feet}{2.5\ in}\\ x=112\ ft[/tex]  

Step 2

width=6 in

Let

if

2.5 in ⇔ 35 ft

6 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{6\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=6\ in\\x*2.5\ in=6\ in *35\ feet\\x=\frac{6\ in *35\ feet}{2.5\ in}\\ x=84\ ft[/tex]  

Step 2

find the perimeter using

Perimeter = 2*length +2* width

replacing

Perimeter= 2*112 ft +2* 84 ft

Perimeter=224 ft +168 ft

Perimeter=392 ft

Have a nice day

Answer:

4/5 pi ,  14pi/5, etc

-16pi/5, -26pi/5, etc

Step-by-step explanation:

To find coterminal angles you add or subtract 2pi from the angle

Rewrite 2pi with a common denominator of 5

2pi * 5/5 = 10pi/5

-6/5 *pi + 10pi/5  = 4/5 pi

4/5pi + 10pi/5 = 14pi/5

etc

you can keep adding 2pi

or you can subtract 2pi

-6pi/5 - 10pi/5 = -16pi/5

-16pi/5 - 10pi/5 = -26pi/5

etc

you can keep subtracting 2pi

Answer:

yes

Step-by-step explanation:

3x × 2x can be broken down as

3 × x × 2 × x = 3 × 2 × x × x = 6 × x² = 6x²

Answer: (C) 1

Step-by-step explanation:

The question is asking which y-value are not represented in the graph.  IN other words, they are asking for which values are not included in the range.

You can do this by graphing the equations:

y = x + 2    for x ≥ 0     has a y-intercept of +2 with y-values increasing

y = x - 2     for x < 0     has a y-intercept of -2 with y-values decreasing

Therefore, there are no y-values between +2 and -2 (including -2). The only option provided between these values is 1, which is option C.

Step-by-step explanation:

The given function is an increasing piecewise function with a jump at x=0 from

f(0-) = -2 to f(0)=+2.

Hence values of f(x) in the interval (-2,+2] cannot be achieved, since

for all x<0, f(x)<-2, and

for all x>=0, f(x)>= +2.

See attached graph for visual explanation.

Answer:

Step-by-step explanation:420÷24=20, so 2 sides are 20, and 2 sides are 24. 20+20+24+24=88 feet of fencing